Educational device for demonstrating nonstandard counting procedures

ABSTRACT

The invention is an educational device for explicitly demonstrating various operations with nonstandard counting procedures, mainly extending binary sequences by an additional digit for each sequence while remaining consistent with hereditary properties residing in the original or challenge sequence. 
     Illustrated in an inscribed sequence with sixteen binary digits and its derived sub-sequence with fifteen binary digits in a configuration for testing values of a variable denoted by the letter `T.`The letter `T` is inscribed upon a plate which indicates the exact position into which a new trial binary digit may be incorporated into the subsequence thereby extending the challenge binary sequence.

BACKGROUND FIELD OF INVENTION

Herein is described an invented device for the educational purpose ofdemonstrating various operations with nonstandard counting procedures,mainly extending binary and other types of sequences by an additionaldigit or symbol to remain consistent with hereditary properties residingin the original or challenge sequence.

My methods and embodiments for extending sequences with deep hereditarystructure have evolved from studies with continuous systems andgeneralized for discrete behavior.

For particularized versions of the original conceptual experiments, seemy "Application of a Block-Wiener Mapping to a Homeostatic LearningSystem," Journal of Cybernetics 1971, 1,3, pp64-78. For sequences withinteresting hereditary properties, see Sir Karl Popper's book: The Logicof Scientific Discovery, wherein lie many examples.

DRAWINGS FIGURES

FIG. 1 shows an inscribed challenge binary sequence and challenge binarysub-sequence and configuration for commencing extension.

FIG. 2 shows advanced stage of determining a fit suitable for extensionby using letter `T` as a variable.

Two-piece Device--Description

FIG. 1 shows a two-piece educational device according to the preferredembodiment of the invention, one piece being composed of four unitsbound into a single unit.

The device comprises in part a primary row of thin metal plates 11soldered together into a unit. The primary row 11 of sixteen platesforms a primary challenge binary sequence of sixteen binary digits, onesand zeros, inscribed upon the plates, including the leftmost primaryplate 13 of the primary binary challenge sequence containing the binarydigit `1` and the right-most primary plate containing the binary digit`1`. The left-most plate 13 and the right -most plate 15 in the primaryrow of plates 11 and plates of the primary row 11 which lie intermediateto them form in precisely prescribed order reading conventionally fromleft to right the primary challenge binary sequence which is:

    1001010000111101

An exposed portion of a primary platen 15 results when the primary rowof plates 11 almost but not totally covers it, leaving a small margin onthe right-hand side of said primary platen to the immediate right of theprimary row of plates 11. The primary row of plates 11 is permanentlyaffixed to the said primary platen.

The invented device comprises also a secondary row of thin metal plates21 soldered together into a unit. The secondary row of plates 21 forms asecondary challenge binary subsequence of fifteen binary digits, onesand zeros, inscribed upon the plates, including the left-most secondaryplate 23 of the secondary challenge binary sub-sequence containing thebinary digit `0` and the right-most plate 25 of the secondary row ofplates 21 inscribed with the binary digit `1`. From left to right thesecondary challenge binary sequence reads as follows:

    001010000111101

An exposed portion of a secondary platen 25 results when the secondaryrow of plates 21 does not totally cover it, leaving a small margin onthe right-hand side of said secondary platen to the immediate right ofthe secondary row of plates 21. The secondary row of plates 21 ispermanently affixed to the secondary platen as a unit.

The secondary platen with its affixed secondary row of plates 21 as aunit is in turn affixed to the primary platen as a unit with its affixedprimary row of plates 11 as a unit. Thus the said primary platen withits attached primary row of plates 11 and the said secondary platen withits attached secondary row of plates 21 are affixed to each other into asingle unit of the two-piece unit.

The primary platen and the secondary platen are aligned as shown in FIG.1 with the righthand edge of the left-most plate 13 aligned collinearlywith the left-most edge of the left-most plate 23 of the secondary row21 of plates. Plate by plate the primary row 11 and the secondary row 21are aligned with a single plate of the secondary row 21 of platesappearing to be missing to give a row of plates only fifteen in number.The locus for the missing plate is the space immediately left of theleft-most plate that actually appears, namely plate 23, the left-mostplate of the secondary row. The plate appearing to be missing is a copyof the left-most plate 13 of the primary row of plates 11, which hasinscribed upon it the binary digit `1`. Each of the other plates of theprimary challenge binary sequence has its exact counterpart in the planeof the paper of FIG. 1 with its duplicate plate enscribed with the samebinary digit. To add a sixteenth digit and thereby increase thesecondary challenge binary sub-sequence from fifteen to sixteen digitsis equivalent to adding one more digit to the primary challenge engebinary digits, giving the primary challenge binary sequence a new digitfor which it is a query of whether it may in fact be the same binarydigit as the digit inscribed on the left-most plate 13 of the primaryrow of plates, exactly identical to the digit appearing to be missingfrom the secondary challenge binary sub-sequence on the left-most side,only to have been restored as the right-most digit inscribed on theright-most plate 25 of the secondary row of plates in this case.

The other piece of the two-piece device comprises a single thin metalblank metal plate 30, with no other inscription of any kind inscribedtheron. As FIG. 1 shows, blank plate 30 is situated to the right at ashort distance from the right-hand edge of the right-most plate 25 ofthe secondary row 21.

The said distance of separation of the blank plate 30 from the secondaryrow 21 of plates is equivalent to the width of the exposed portion 19 ofthe secondary platen.

FIG. 1 and FIG. 2 differ only in the occurrence of the blank plate 30 inFIG. 1 and the occurrence of a plate 32 of FIG. 2, which is inscribedwith a letter variable `T` and situated exactly in the positiondescribed to be to the right of the secondary row 21 of metal plates.

Two-piece Device--Operation

A two-piece educational device shown in FIG. 1 will demonstrate theappropriate manner in which to extend correctly a challenge binarysequence by one more digit so as to be consistent with the hereditaryproperties residing in the said challenge sequence. Users will find theembodiment of the method of demonstration most useful where non-standardcounting numbers are involved.

To demonstrate the extending of the challenge binary sequence:

    1001010000111101

the user should refer to FIG. 1 and should use the blank plate 30 as anindicator of the exact position into which the new binary digit shouldbe incorporated.

Specification of said exact positioning must be in relation to theprimary platen exposed portion 19 on the right for the platenaccommodates the primary row 11 of metal plates bearing the sixteenbinary digits of the challenge binary sequence:

    1001010000111101

and must also be in relation to the secondary platen exposed portion 29on the right for the platen accommodates the secondary row 21 of platesbearing the fifteen binary digits of the challenge binary sub-sequence:

    001010000111101

With the blank plate 30 positioned in the appropriate relationship asillustrated in FIG. 1, the plate 32 inscribed with the variable letter`T` may now be substituted for blank plate 30. The plate 32 with `T` forTrial, permits substitution and preliminary trial and testing, ifnecessary, with either a thin metal plate inscribed with a zero orinscribed with a one, using uniformly manufactured plates as heretoforeemployed in the device. In the same binary case as before the correctfit is found for the variable letter `T` to have the value `1`, andaccordingly a plate so inscribed remaining in position with the platen13 which is primary and with the platen 23 which is secondary permits noerror or contradiction, thus consistency with respect to the hereditaryproperties both the challenge binary sequence and the challenge binarysub-sequence.

While the above description contains many specifications, these shouldnot be in any way conceived as limitations on the scope of the inventionbut merely examples of a application and preferred embodiments whichhave an inner logic inherent to correctness of the procedures employed.Skilled artisans will see many possibilites in the richness ofhereditary theory and nonstandard counting theory. Plates and platensmay be made of many kinds of rigid or flexible imprintable materialswhich is of no consequence to the performance of correctly materializingan extension of hereditary properties. Also any set of whole numbers orof course also finite set of differentiated symbols will do to constructchallenge sequences and their derived challenge sub-sequences. It is tobe hoped that the reader will determine the scope of the invention byusages in the claims section and their legal equivalents and not by theexamples and discussion given, alone.

I claim:
 1. An educational device for extending sequences comprising;afirst platen accomodating a row of a plurality of first plates securedtogether and inscribed with a challenge numerical sequence; a secondplaten accomodating a row of a plurality of second plates securedtogether and inscribed with a challenge numerical sub-sequence; saidfirst and second platens being secured together to function as a unit,with said second platen being offset to the right with respect to saidfirst platen by one digit position of said sequence; and a third platepositioned to the right of said second platen, said third plate servingas a means of preparing for the continuation of said challenge numericalsub-sequence.
 2. The device of claim 1 wherein said numerical sequenceand numerical sub-sequence are a binary sequence and a binarysub-sequence.
 3. The device of claim 1 wherein said third plate isblank.
 4. The device of claim 1 further comprising a fourth plateinscribed with letter T, said fourth plate being substituted for saidthird plate and serving as a means of testing for the continuation ofsaid challenge binary sequence.
 5. The device of claim 1 wherein thechallenge sequence in an n-ary sequence for any n, whole number.
 6. Thedevice of claim 1, wherein the challenge sequence comprises any finitenumber of any differentiated symbols.
 7. The device of claim 1 whereinsaid first and second platens and said first and second pluralities ofplates are metal.